Thursday, August 15, 2013

History’s Nightmare

Filed under: General — m759 @ 7:20 AM


See Quine + Boxer in this journal.

Tuesday, April 12, 2011

History: The Nightmare Continues

Filed under: General — m759 @ 9:29 PM

From the AP "Today in History" column for April 12—

On this date:

In 1606, England's King James I decreed the design of the original Union Flag, which combined the flags of England and Scotland.


The 1606 Union Flag incorporated the crosses of St. George (England) and St. Andrew (Scotland).
This suggests some notes on graphic design.

See The Double Cross.

Sunday, October 28, 2018

History 101

Filed under: General — Tags: — m759 @ 1:01 PM

 181028-Interrobang-Wikipedia.jpg (229×524)

'Pinter's hallmark,' according to Harlan Ellison

Monday, October 15, 2018

History at Bellevue

Filed under: General,Geometry — Tags: , — m759 @ 9:38 PM

The previous post, "Tesserae for a Tesseract," contains the following
passage from a 1987 review of a book about Finnegans Wake

"Basically, Mr. Bishop sees the text from above
and as a whole — less as a sequential story than
as a box of pied type or tesserae for a mosaic,
materials for a pattern to be made."

A set of 16 of the Wechsler cubes below are tesserae that 
may be used to make patterns in the Galois tesseract.

Another Bellevue story —

History, Stephen said, is a nightmare
from which I am trying to awake.”

— James Joyce, Ulysses

Friday, July 7, 2017

Psycho History

Filed under: General — Tags: — m759 @ 6:00 PM

The title was suggested by the term “psychohistory” in
the Foundation  novels of Isaac Asimov. See the previous post.

See also a 2010 New York Times  review of
DeLillo’s novel Point Omega . The review is titled,
without any other reference to L’Engle’s classic tale
of the same name, “A Wrinkle in Time.”

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Related material: The Crosswicks Curse.

Friday, December 23, 2016

Memory, History, Geometry

Filed under: General,Geometry — Tags: — m759 @ 6:48 PM


Code Blue

Update of 7:04 PM ET —

The source of the 404 message in the browsing history above
was the footnote below:

Friday, December 16, 2016

Memory, History, Geometry

Filed under: General,Geometry — Tags: — m759 @ 9:48 AM

These are Rothko's Swamps .

See a Log24 search for related meditations.

For all three topics combined, see Coxeter —

" There is a pleasantly discursive treatment 
of Pontius Pilate’s unanswered question
‘What is truth?’ "

— Coxeter, 1987, introduction to Trudeau’s
     The Non-Euclidean Revolution

Update of 10 AM ET —  Related material, with an elementary example:

Posts tagged "Defining Form." The example —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

Tuesday, September 15, 2015

Joyce’s Nightmare

Filed under: General — m759 @ 2:42 PM


Today's AP history notes

The above image suggests a search for Missing Art.

Tuesday, June 2, 2015


Filed under: General — m759 @ 4:21 PM

Continued from August 5, 2002

See also Venn's Trinity ("diamonds and rust") and a Monday death.

Saturday, August 18, 2012

Nightmare Alley

Filed under: General — m759 @ 11:00 PM

"History instructs. History also has
a very dark sense of humor.
Irish history, especially."

John Kelly in The Daily Beast  this morning

See also Joyce's Nightmare and
Nightmare Alley in this journal.

Wednesday, July 18, 2012

Joyce’s Nightmare

Filed under: General — m759 @ 6:00 PM

"History, Stephen said…."

For a black widow —

See history in today's Boston.com
and Waldorf in this journal.

Sunday, April 5, 2020

Plan 9 from The New York Times

Filed under: General — Tags: — m759 @ 12:02 PM

Click the image above for a tweet on the advertised IQ test.

Click the image below for the tweet’s details of the IQ test’s billing plan.

The Ghost in the Shell

Filed under: General — Tags: — m759 @ 10:57 AM

Tuesday, September 12, 2017


Filed under: General,Geometry — Tags: — m759 @ 12:18 PM

"Truth and clarity remained his paramount goals…"

— Benedict Nightingale in today's online New York TImes  on an
English theatre director, founder of the Royal Shakespeare Company,
who reportedly died yesterday at 86.

See also Paramount in this  journal.

Monday, September 11, 2017

New Depth

Filed under: General,Geometry — Tags: — m759 @ 9:48 PM

A sentence from the New York Times Wire  discussed in the previous post

NYT Wire on Len Wein: 'Through characters like Wolverine and Swamp Thing, he helped bring a new depth to his art form.'

"Through characters like Wolverine and Swamp Thing,
he helped bring a new depth to his art form."

For Wolverine and Swamp Thing in posts related to a different
art form — geometry — see …

Friday, July 7, 2017

A Prime Radiant for Krugman

Filed under: General — Tags: , — m759 @ 6:00 AM

Paul Krugman:
Asimov’s Foundation  novels grounded my economics

In the Foundation  novels of Isaac Asimov

“The Prime Radiant can be adjusted to your mind, and all
corrections and additions can be made through mental rapport.
There will be nothing to indicate that the correction or addition
is yours. In all the history of the Plan there has been no
personalization. It is rather a creation of all of us together.
Do you understand?”

“Yes, Speaker!”

— Isaac Asimov, Second Foundation , Ch. 8: Seldon’s Plan

Before time began, there was the Cube.

See also Transformers in this journal.

Sunday, March 26, 2017

Seagram Studies

Filed under: General,Geometry — Tags: — m759 @ 9:00 PM

From a search in this journal for Seagram + Tradition

Related art:  Saturday afternoon's Twin Pillars of Symmetry.

Saturday, March 25, 2017

Twin Pillars of Symmetry

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

The phrase "twin pillars" in a New York Times  Fashion & Style
article today suggests a look at another pair of pillars —

This pair, from the realm of memory, history, and geometry disparaged
by the late painter Mark Rothko, might be viewed by Rothko
as  "parodies of ideas (which are ghosts)." (See the previous post.)

For a relationship between a 3-dimensional simplex and the {4, 3, 3},
see my note from May 21, 2014, on the tetrahedron and the tesseract.

Like Decorations in a Cartoon Graveyard

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM

Continued from April 11, 2016, and from

A tribute to Rothko suggested by the previous post

For the idea  of Rothko's obstacles, see Hexagram 39 in this journal.

Sunday, December 25, 2016

Credit Where Due

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

See also Robert M. Pirsig in this journal on Dec. 26, 2012.

Saturday, December 24, 2016

Early X Piece

Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

In memory of an American artist whose work resembles that of
the Soviet constructivist Karl Ioganson (c. 1890-1929).

The American artist reportedly died on Thursday, Dec. 22, 2016.

"In fact, the (re-)discovery of this novel structural principle was made in 1948-49 by a young American artist whom Koleichuk also mentions, Kenneth Snelson. In the summer of 1948, Snelson had gone to study with Joseph Albers who was then teaching at Black Mountain College. . . . One of the first works he made upon his return home was Early X Piece  which he dates to December 1948 . . . . "

— "In the Laboratory of Constructivism:
      Karl Ioganson's Cold Structures,"
      by Maria GoughOCTOBER  Magazine, MIT,
      Issue 84, Spring 1998, pp. 91-117

The word "constructivism" also refers to a philosophy of mathematics.
See a Log24 post, "Constructivist Witness,"  of 1 AM ET on the above
date of death.

Thursday, December 22, 2016

The Laugh-Hospital

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Constructivism in mathematics and the laughing academy

See also, from the above publication date, Hudson's Inscape.
The inscape is illustrated in posts now tagged Laughing Academy.

Constructivist Witness

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM

The title refers to a philosophy of mathematics.

For those who prefer metaphor Folk Etymology.

See also Stages of Math at Princeton's  
Institute for Advanced Study in March 2013 —

— and in this journal starting in August 2014.

Monday, December 19, 2016


Filed under: General,Geometry — Tags: , — m759 @ 10:25 PM

See also all posts now tagged Memory, History, Geometry.

Tetrahedral Cayley-Salmon Model

Filed under: General,Geometry — Tags: , — m759 @ 9:38 AM

The figure below is one approach to the exercise
posted here on December 10, 2016.

Tetrahedral model (minus six lines) of the large Desargues configuration

Some background from earlier posts —

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

Click the image below to enlarge it.

Polster's tetrahedral model of the small Desargues configuration

Sunday, December 18, 2016

Two Models of the Small Desargues Configuration

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Click image to enlarge.

Polster's tetrahedral model of the small Desargues configuration

See also the large  Desargues configuration in this journal.

Saturday, December 17, 2016

Tetrahedral Death Star

Filed under: General,Geometry — Tags: , — m759 @ 10:00 PM

Continuing the "Memory, History, Geometry" theme
from yesterday

See Tetrahedral,  Oblivion,  and Tetrahedral Oblivion.

IMAGE- From 'Oblivion' (2013), the Mother Ship

"Welcome home, Jack."

Friday, December 16, 2016

Read Something That Means Something

Filed under: General,Geometry — Tags: , — m759 @ 5:29 PM

Rothko’s Swamps

Filed under: General,Geometry — Tags: , — m759 @ 2:45 AM

“… you don’t write off an aging loved one
just because he or she becomes cranky.”

— Peter Schjeldahl on Rothko in The New Yorker ,
issue dated December 19 & 26, 2016, page 27

He was cranky in his forties too —

See Rothko + Swamp in this journal.

Related attitude —

From Subway Art for Times Square Church , Nov. 7

Tuesday, December 13, 2016

The Thirteenth Novel

Filed under: General,Geometry — Tags: — m759 @ 4:00 PM

John Updike on Don DeLillo's thirteenth novel, Cosmopolis

" DeLillo’s post-Christian search for 'an order at some deep level'
has brought him to global computerization:
'the zero-oneness of the world, the digital imperative . . . . ' "

The New Yorker , issue dated March 31, 2003

On that date ….

Related remark —

" There is a pleasantly discursive treatment 
of Pontius Pilate’s unanswered question
‘What is truth?’ "

— Coxeter, 1987, introduction to Trudeau’s
     The Non-Euclidean Revolution

Saturday, December 10, 2016

Folk Etymology

Images from Burkard Polster's Geometrical Picture Book

See as well in this journal the large  Desargues configuration, with
15 points and 20 lines instead of 10 points and 10 lines as above.

Exercise:  Can the large Desargues configuration be formed
by adding 5 points and 10 lines to the above Polster model
of the small configuration in such a way as to preserve
the small-configuration model's striking symmetry?  
(Note: The related figure below from May 21, 2014, is not
necessarily very helpful. Try the Wolfram Demonstrations
, which requires a free player download.)

Labeling the Tetrahedral Model (Click to enlarge) —

Related folk etymology (see point a  above) —

Related literature —

The concept  of "fire in the center" at The New Yorker , 
issue dated December 12, 2016, on pages 38-39 in the
poem by Marsha de la O titled "A Natural History of Light."

Cézanne's Greetings.

Sunday, February 8, 2015

Hungarian Phenomenon

Filed under: General — Tags: , , , — m759 @ 2:07 PM

For Autism Sunday —

Mathematician John von Neumann
reportedly died on this date.

“He belonged  to that so-called
Hungarian phenomenon….”

A webpage titled
“Von Neumann, Jewish Catholic”

Illustrations of another Hungarian phenomenon:

IMAGE- Anthony Hopkins exorcises a Rubik cube

Saturday, September 7, 2013

Structure and Character

Filed under: General — Tags: , — m759 @ 9:00 PM

(Continued from May 4, 2013)

“I saw a werewolf with a Chinese menu in his hand
Walking through the streets of Soho in the rain”

Warren Zevon

“It is well
That London, lair of sudden
Male and female darknesses,
Has broken her spell.”

— D. H. Lawrence in a poem on a London blackout
during a bombing raid in 1917. See also today’s previous
posts, Down Under and Howl.

Backstory— Recall, from history’s nightmare on this date,
the Battle of Borodino and the second  London Blitz.

Saturday, May 11, 2013


Filed under: General,Geometry — Tags: , , — m759 @ 12:00 PM

Promotional description of a new book:

“Like Gödel, Escher, Bach  before it, Surfaces and Essences  will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”

“Like Gödel, Escher, Bach  before it….”

Or like Metamagical Themas .

Rubik core:

Swarthmore Cube Project, 2008

Non- Rubik cores:

Of the odd  nxnxn cube:

Of the even  nxnxn cube:

The image “http://www.log24.com/theory/images/cube2x2x2.gif” cannot be displayed, because it contains errors.

Related material: The Eightfold Cube and

“A core component in the construction
is a 3-dimensional vector space  over F.”

—  Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)

Saturday, November 17, 2012

Hey RAM*

Filed under: General — m759 @ 12:00 PM

Last evening's NY Lottery numbers
985 and 3274, interpreted as the
numbers of Log24 posts, suggest
a look at Joyce's nightmarehistory.

* The title refers both to a film and to
   a Log24 post, Random Access Memory.

Tuesday, October 23, 2012


Filed under: General — m759 @ 6:30 AM


A new Wikipedia page was created on Oct. 9—

"This page was last modified on 9 October 2012 at 19:54."

This, and a long-running musical, suggest…

"Try to remember the kind of September…"

LIFE Magazine for September 6, 1954, provides
one view of the kind of September when I was
twelve years old. (Also that September, Mitt Romney
was seven. President Obama was born later.)

Top of Life Magazine cover, September 6, 1954

This suggests James Joyce's nightmare view of history.

For some other views of 1954, see selected posts in this  journal
 that mention that year.

See also IMDb on Grace Kelly that year, and a related theological
reflection from Holy Cross Day, 2002.

Saturday, September 24, 2011

Ariadne and the Exorcist

Filed under: General — Tags: — m759 @ 12:00 PM

The title describes two philosophical events (one major, one minor) from the same day— Thursday, July 5, 2007. Some background from 2001:

"Are the finite simple groups, like the prime numbers, jewels strung on an as-yet invisible thread? And will this thread lead us out of the current labyrinthine proof to a radically new proof of the Classification Theorem?" (p. 345)

— Ronald Solomon,  "A Brief History of the Classification of Finite Simple Groups," Bulletin of the American Mathematical Society , Vol. 38 No. 3 (July 2001), pp. 315-352

The major event— On July 5, 2007, Cambridge University Press published Robert T. Curtis's Symmetric Generation of Groups.*

Curtis's book does not purport to lead us out of Solomon's labyrinth, but its publication date may furnish a Jungian synchronistic clue to help in exiting another  nightmare labyrinth— that of postmodernist nominalism.

The minor event— The posting of Their Name is Legion in this journal on July 5, 2007.

* This is the date given by Amazon.co.uk and by BookDepository.com. Other sources give a later July date, perhaps applicable to the book's publication in the U.S. rather than Britain.

Friday, September 9, 2011

Galois vs. Rubik

Filed under: General,Geometry — Tags: , , , — m759 @ 2:56 PM

(Continued from Abel Prize, August 26)

IMAGE- Elementary Galois Geometry over GF(3)

The situation is rather different when the
underlying Galois field has two rather than
three elements… See Galois Geometry.

Image-- Sugar cube in coffee, from 'Bleu'

The coffee scene from “Bleu”

Related material from this journal:

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

Wednesday, March 9, 2011

The Uploading

Filed under: General — m759 @ 9:00 AM

Philosophy versus Stories


The above uploading was done on December 10th, 2006.
For some context, see the Log24 posts for December 2006.

See also the German version of a nursery rhyme
that one commenter has called "morbid and horrifying"—

"Dein Vater sitzt auf der Schwelle:
  Flieg in Himmel aus der Hölle."

The rhyme suggests characters in the novel The Quest for the 36
related to the Triangle Shirtwaist Factory fire often recalled during
women's history month. It also suggests the oeuvre  of Stephen King.

History, Stephen said, is a nightmare
from which I am trying to awake.”

Monday, March 2, 2009

Monday March 2, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:30 AM

Joyce’s Nightmare

Today in History – March 2

Today is Monday, March 2, the 61st day of 2009. There are 304 days left in the year.

Today’s Highlight in History:

On March 2, 1939, Roman Catholic Cardinal Eugenio Pacelli was elected Pope on his 63rd birthday; he took the name Pius XII.

Angels and Demons, Illuminati Diamond, pages 359-360

Log24 on June 9, 2008

From Gravity’s Rainbow (Penguin Classics, 1995), page 563:

“He brings out the mandala he found.
‘What’s it mean?’

Slothrop gives him the mandala. He hopes it will work like the mantra that Enzian told him once, mba-kayere (I am passed over), mba-kayere… a spell […]. A mezuzah. Safe passage through a bad night….”

In lieu of Slothrop’s mandala, here is another…

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton’s Thought,
by B. J. T. Dobbs,
Cambridge University Press,
2002, p. 85


Related mandalas:Diamond arrangement of the four elements

Logo by Steven H. Cullinane for website on finite geometry


For further details,
click on any of the
three mandalas above.

Angels and Demons cross within a diamond (page 306), and Finite Geometry logo

Happy birthday to
Tom Wolfe, author of
The Painted Word.

Tuesday, June 17, 2008

Tuesday June 17, 2008

Filed under: General — m759 @ 7:01 AM
Nightmare Alley

History, Stephen said,
is a nightmare from which
I am trying to awake.”


Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.


Black disc from end of Ch. 17 in Ulysses

Ulysses, conclusion of Chapter 17

When in Rome

His manner was all charm
and grace; pure cafe society….

He purred a chuckle.
“My place. If you want to come,
I’ll show you.”

“Love to. The Luogo Nero?
The Black Place?”

“That’s what the locals call it.
It’s really Buoco Nero,
the Black Hole.”

Psychoshop, by
Alfred Bester and Roger Zelazny

In memory of
special effects wizard
Stan Winston,
who died Sunday at 62:


“The energetic Winston
was always looking
 to the next project.”

— Today’s LA Times,
story by
Dennis McLellan

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 9:00 AM
Wechsler Cubes
“Confusion is nothing new.”
— Song lyric, Cyndi Lauper
Part I:
Magister Ludi

Hermann Hesse’s 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

“For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar’s Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors.”

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

“Bill worked long hours on a series of autonomous pieces about numbers. Like O’s Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is “free.” Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn’t visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe’s color wheel and in Alfred Jensen’s use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn’t bother with the poet’s meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page.”

Part III:
Wechsler Cubes(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) —

From 2002:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.

Part IV:
A Magic Gallery
Log24, March 4, 2004


Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:

Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
auf weiss
schaffen wir neue Welten
oder gar Universen

 Numbers and Names,
Wording and Words

With numbers and names
we measure heaven and earth
on white
we create new worlds
and universes

English translation
by Catherine Schelbert
A related poem:

by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone’s command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens’
feet upon the snow.
He’d hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He’d see the way love burns
and anguish trembles,
He’d wonder, laugh,
shake with fear and weep
because beyond this cipher’s
cross-barred keep
he’d see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
He’d think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He’ll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
Buchstaben,” from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Tuesday, August 7, 2007

Tuesday August 7, 2007

Filed under: General — Tags: — m759 @ 6:25 PM
In memory of

Atle Selberg, mathematician,
dead at 90 on August 6, 2007

According to the
American Mathematical Society,
Selberg died, like André Weil, on
 the Feast of the Metamorphosis.


The image “http://www.log24.com/log/pix07A/070807-escher.jpg” cannot be displayed, because it contains errors.

Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye.

— Steven H. Cullinane, Nov. 7, 1986

Read more.

For further views of
the Amalfi coast, site of
the above Escher scene,
see the film "A Good Woman"
(made in 2004, released in 2006)
starring Scarlett Johansson–

The image “http://www.log24.com/log/pix07A/070807-GoodWoman.jpg” cannot be displayed, because it contains errors.

Scene from "A Good Woman"

— and the following from

The Feast of St. Luke, 2005:
The image “http://www.log24.com/log/pix05B/051018-Atrani2.jpg” cannot be displayed, because it contains errors.
Collegiate Church of
St. Mary Magdalene,
Atrani, Amalfi Coast, Italy:
"An interior made exterior"
— Wallace Stevens

Monday, June 18, 2007

Monday June 18, 2007

Filed under: General — m759 @ 1:00 PM
Nightmare Lessons

We are going to keep doing this
until we get it right.”
Log24 on June 15  

Obituaries in the News


Published: Monday, June 18, 2007
in The New York Times

Filed at 6:13 a.m. ET

Norman Hackerman

“AUSTIN, Texas (AP) — Norman Hackerman, a chemist … died Saturday [June 16] …. He was 95. … He taught chemistry … before joining the Manhattan Project to develop a nuclear weapon during World War II.”

The date of Hackerman’s death is celebrated in Ireland as Bloomsday— the day on which, in 1904, the events of James Joyce’s novel Ulysses came to pass.

From Log24 on Bloomsday 2007:

Scene from  
Behind the Lid” —

Scene from Behind the Lid

Photo by Richard Termine

“Behind the Lid” is an avant-garde production featuring scenes from the author’s life presented in the form of dreams.

Those who like such scenes may consult past Log24 entries.  They will find, for instance, the following, commemorating a death which, like Hackerman’s, occurred on a Bloomsday:

The image “http://www.log24.com/log/pix04A/040626-Bloomsday.jpg” cannot be displayed, because it contains errors.

Click on the picture for details.

History, Stephen said,
is a nightmare
from which I am
trying to awake.”


Wednesday, March 21, 2007

Wednesday March 21, 2007

Filed under: General,Geometry — Tags: — m759 @ 7:29 PM
Art Appreciation

A rectangle in memory of
Harvard mathematician
George Mackey:

The five Log24 entries ending at
7:00 PM on March 14, 2006,
the last day of Mackey's life:

A rectangle in memory of
artist Mark Rothko:

The image “http://www.log24.com/log/pix07/070321-Rothko.jpg” cannot be displayed, because it contains errors.

  Rothko Painting
Is Up for Auction

March 21, 5:35 PM ET

"David Rockefeller plans to sell
a seminal painting by Mark Rothko
for what Sotheby's hopes will be
more than $40 million. Above,
a detail from the painting."

From the story:

"Mr. Rockefeller has owned the
painting since 1960, when he
bought it for less than $10,000….
He said that in November, during a
periodic appraisal of his art collection,
he noticed to his surprise that of all
his paintings, the Rothko had
appreciated in value the most.
'That got me thinking,' he said."

Art appreciation:

When Crayolas worked, I dreamed an angel,
a bar of light, your messenger,
beckoning from a wallpaper corner,
blushing in the porcelain gas glow.

When Crayolas worked and chariots swung low,
and America was beautiful and time was slow.

Then all that died in life's longer year.
Autumn came, colors turned sere.
Brittle Crayolas crumbled when touched.
The friends of life were cold and hushed.

Still you were there, shining and warm
behind snow clouds, safe from our harm.
The seed I am again burst out,
drank your heat, suckled your light

in another fair spring to live again
on billowing oceans of bottomless green.

— Excerpt from C. K. Latham's
   When Crayolas Worked,
   from Shiva Dancing:
   The Rothko Chapel Songs,

Sunday, February 18, 2007

Sunday February 18, 2007

Filed under: General — m759 @ 10:30 AM
Further Adventures
in Harvard Iconology

The image “http://www.log24.com/log/pix06A/061001-Langdon2.jpg” cannot be displayed, because it contains errors.

The next novel starring
Robert Langdon, Harvard author
of "the renowned collegiate
texbook Religious Iconology"
is said to be titled
The Solomon Key.

Related material–

The Harvard Crimson online:

Fishburne To Receive Honors at Cultural Rhythms
Acclaimed actor and humanitarian chosen as the Harvard Foundation's Artist of the Year

Friday, February 16, 2007
9:37 PM

Tony and Emmy Award-winning actor Laurence Fishburne will take the stage later this month as the 2007 Artist of the Year during the 22nd annual Cultural Rhythms festival, the Harvard Foundation for Intercultural and Race Relations announced Friday afternoon.

The image “http://www.log24.com/log/pix07/070218-Morpheus.jpg” cannot be displayed, because it contains errors.
as Morpheus

"Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye….

Dabo claves regni caelorum.  By silent shore
Ripples spread from castle rock.  The metaphor
For metamorphosis no keys unlock."

— Steven H. Cullinane,
  November 7, 1986,

More on metamorphosis–

Cat's Yarn
(Log24, June 20, 2006):

"The end is where
   we start from."

T. S. Eliot

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Garfield 2003-06-24

See also:

Zen Koan
  Blue Dream.

Update of 5:24 PM
Feb. 18, 2007:

A Xanga footprint from France
this afternoon (3:47 PM EST)
indicates that someone there
may be interested in the above
poem's "claves regni caelorum."

The visitor from France viewed
"Windmills" (Nov. 15, 2005).
Material related to that entry
may be found in various places
at Log24.com.  See particularly
"Shine On, Hermann Weyl," and
entries for Women's History
last year that include
"Christ at the Lapin Agile."

Sunday, July 30, 2006

Sunday July 30, 2006

Filed under: General — m759 @ 2:56 AM


From “Today in History,” by The Associated Press–

On this date (July 30):

In 1864, during the Civil War, Union forces tried to take Petersburg, Va., by exploding a mine under Confederate defense lines; the attack failed.”

“A nightmare” — Ulysses

Men ask the way to Cold Mountain.
Cold Mountain: there’s no through trail.
Han Shan

See also July 3, 2005.

Thursday, May 27, 2004

Thursday May 27, 2004

Filed under: General — Tags: — m759 @ 10:10 AM


On the poetry of Geoffrey Hill:

"… why read him? Because of the things he writes about—war and peace and sacrifice, and the search for meaning and the truths of the heart, and for that haunting sense that, in spite of war and terror and the indifferences that make up our daily hells, there really is some grander reality, some ineluctable presence we keep touching. There remains in Hill the daunting possibility that it may actually all cohere in the end, or at least enough of it to keep us searching for more.

There is a hard edge to Hill, a strong Calvinist streak in him, and an intelligence that reminds one of Milton….."

— Paul Mariani, review in America of Geoffrey Hill's The Orchards of Syon

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses, Proteus chapter

"Time has been unfolded into space."

James O. Coplien, Bell Labs

"Pattern and symmetry are closely related."

James O. Coplien on Symmetry Breaking

"… as the critic S. L. Goldberg puts it, 'the chapter explores the Protean transformations of matter in time . . . apprehensible only in the condition of flux . . . as object . . . and Stephen himself, as subject. In the one aspect Stephen is seeking the principles of change and the underlying substance of sensory experience; in the other, he is seeking his self among its temporal manifestations'….

— Goldberg, S.L. 'Homer and the Nightmare of History.' Modern Critical Views: James Joyce. Ed. Harold Bloom. New York: Chelsea House, 1986. 21-38."

from the Choate site of David M. Loeb

In summary:


James Joyce


See also Time Fold.

(By the way, Jorn Barger seems
to have emerged from seclusion.)


Thursday, April 22, 2004

Thursday April 22, 2004

Filed under: General,Geometry — Tags: — m759 @ 10:07 PM


"It's become our form of modern classicism."

— Nancy Spector in 
   the New York Times of April 23, 2004

Part I: Aesthetics

In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website

"Minimalism refers to painting or sculpture

  1. made with an extreme economy of means
  2. and reduced to the essentials of geometric abstraction….
  3. Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
  4. mathematically regular compositions, often based on a grid….
  5. the reduction to pure self-referential form, emptied of all external references….
  6. In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
  7. The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."

Discuss these seven points
in relation to the following:

by S. H. Cullinane

Logos and Logic

Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art

Michael Kimmelman's
remarks on ideas in art 

Notes on ideas and art

of the 4×4 square

The Grid of Time

Judgment Day
(2003, 10/07)

Part II: Theology

Today's previous entry, "Skylark," concluded with an invocation of the Lord.   Of course, the Lord one expects may not be the Lord that appears.

 John Barth on minimalism:

"… the idea that, in art at least, less is more.

It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "

Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:

"He would think about Bert.  Bert was an interesting man.  Bert had said something about the way a gambler wants to lose.  That did not make sense.  Anyway, he did not want to think about it.  It was dark now, but the air was still hot.  He realized that he was sweating, forced himself to slow down the walking.  Some children were playing a game with a ball, in the street, hitting it against the side of a building.  He wanted to see Sarah.

When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table.  She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her.  The room was hot; she had opened the windows, but the air was still.  The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom.  The only light in the room was from the lamp over the couch where she was reading.

He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  'What's the book,' he said, trying to make his voice conversational.  But it sounded loud in the room, and hard.

She blinked up at him, smiled sleepily, and said nothing.

'What's the book?'  His voice had an edge now.

'Oh,' she said.  'It's Kierkegaard.  Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.

'What's that?' he said.

'Well, I don't exactly know, myself."  Her voice was soft and thick.

He turned his face away from her again, not knowing what he was angry with.  'What does that mean, you don't know, yourself?'

She blinked at him.  'It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it once, and that's what I'm doing.  Reading it.'

He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not.  'That's great,' he said, and it came out with more irritation than he had intended.

She closed the book, tucked it beside her on the couch.  She folded her arms around her, hugging herself, smiling at him.  'I guess this isn't your night, Eddie.  Why don't we have a drink?'

'No.'  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.

Her smile, her drunk, amused smile, did not change.  'Then let's talk about something else,' she said.  'What about that case you have?  What's in it?'  Her voice was not prying, only friendly, 'Pencils?'

'That's it,' he said.  'Pencils.'

She raised her eyebrows slightly.  Her voice seemed thick.  'What's in it, Eddie?'

'Figure it out yourself.'  He tossed the case on the couch."

— Walter Tevis, The Hustler, 1959,
    Chapter 11

See, too, the invocation of Apollo in

A Mass for Lucero, as well as 

Wednesday 15 January 2003

"The invocation of the Lord is relentless…."


Wednesday 15 January 2003

Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."

Monday, April 19, 2004

Monday April 19, 2004

Filed under: General — m759 @ 7:59 PM

Cartesian Theatre

From aldaily.com today:

"If my mind is a tiny theatre I watch in my brain, then there is a tinier mind and theatre inside that mind to see it, and so on forever… more»"

This leads to the dream (or nightmare) of the Cartesian theatre, as pictured by Daniel Dennett.

From websurfing yesterday and today…

The tiny theatre of Ivor Grattan-Guinness:

"… mathematicians often treat history with contempt (unsullied by any practice or even knowledge of it, of course)."

The Rainbow of Mathematics

The contempt for history of the Harvard mathematics department (see previous entry) suggests a phrase….

A search on "Harvard sneer" yields, as the first page found, a memorial to an expert practitioner of the Harvard sneer… Robert Harris Chapman, Professor of English Literature, playwright, theatrical consultant, and founding Director of the Loeb Drama Center from 1960 to 1980.

Continuing the Grattan-Guinness rainbow theme in a tinier theatre, we may picture Chapman's reaction to the current Irish Repertory Theatre production of Finian's Rainbow.  Let us hope it is not a Harvard sneer.

In a yet tinier theatre, we may envision a mathematical version of Finian's Rainbow, with Og the leprechaun played by Andrew P. Ogg.  Ogg would, of course, perform a musical version of his remarks on the Jugendtraum:

"Follow the fellow who follows a dream."

Melissa Errico
in Finian's Rainbow

"Give her a song like…. 'Look to the Rainbow,' and her gleaming soprano effortlessly flies it into the stratosphere where such numbers belong. This is the voice of enchantment…."

Ben Brantley, today's NY Times

For related philosophical remarks on rainbows, infinite regress, and redheads, see

Loretta's Rainbow and

The Leonardo Code.

Friday, June 27, 2003

Friday June 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 6:16 PM

For Fred Sandback:
Time's a Round

The following entry of Feb. 25, 2003, was written for painter Mark Rothko, and may serve as well for minimalist artist Fred Sandback, also connected to the de Menil family of art patrons, who, like Rothko, has killed himself.

Plagued in life by depression — what Styron, quoting Milton, called "darkness visible" — Rothko took his own life on this date [Feb. 25] in 1970.  As a sequel to the previous note, "Song of Not-Self," here are the more cheerful thoughts of the song "Time's a Round," the first of Shiva Dancing: The Rothko Chapel Songs, by C. K. Latham.  See also my comment on the previous entry (7:59 PM).

Time’s a round, time’s a round,
A circle, you see, a circle to be.

— C. K. Latham



The following is from the cover of
"Finnegans Wake: a Symposium,"

a reprint of

Our Exagmination Round His Factification
for Incamination of Work in Progress


Paris, Shakespeare and Company, 1929.

As well as being a memorial to Rothko and Sandback, the above picture may serve to mark the diamond anniversary of a dinner party at Shakespeare and Company on this date in 1928.  (See previous entry.)

A quotation from aaparis.org also seems relevant on this, the date usually given for the death of author Malcolm Lowry, in some of whose footsteps I have walked:

"We are not saints." 

— Chapter V, Alcoholics Anonymous

Thursday, March 6, 2003

Thursday March 6, 2003

Filed under: General,Geometry — Tags: , — m759 @ 2:35 AM


Geometry for Jews

Today is Michelangelo's birthday.

Those who prefer the Sistine Chapel to the Rothko Chapel may invite their Jewish friends to answer the following essay question:

Discuss the geometry underlying the above picture.  How is this geometry related to the work of Jewish artist Sol LeWitt? How is it related to the work of Aryan artist Ernst Witt?  How is it related to the Griess "Monster" sporadic simple group whose elements number 

808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000?

Some background:

Tuesday, February 25, 2003

Tuesday February 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 10:23 PM

For Mark Rothko

Plagued in life by depression — what Styron, quoting Milton, called "darkness visible" — Rothko took his own life on this date in 1970.  As a sequel to the previous note, "Song of Not-Self," here are the more cheerful thoughts of the song "Time's a Round," the first of Shiva Dancing: The Rothko Chapel Songs, by C. K. Latham.  See also my comment on the previous entry (7:59 PM).

Time’s a round, time’s a round,
A circle, you see, a circle to be.

— C. K. Latham



Tuesday February 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 1:44 AM

Song of Not-Self

A critic on the abstract expressionists:

"…they painted that reality — that song of self — with a passion, bravura, and decisiveness unequaled in modern art."

Painter Mark Rothko:

"I don't express myself in painting. 
 I express my not-self."

On this day in 1957, Buddy Holly and his group recorded the hit version of "That'll Be the Day."

On this day in 1970, painter Mark Rothko committed suicide in his New York City studio.

On February 27, 1971, the Rothko Chapel was formally dedicated in Houston, Texas.

On May 26, 1971, Don McLean recorded "American Pie."

Rothko was apparently an alcoholic; whether he spent his last day enacting McLean's lyrics I do not know.

Rothko is said to have written that

"The progression of a painter's work, as it travels in time from point to point, will be toward clarity: toward the elimination of all obstacles between the painter and the idea, and between the idea and the observer. As examples of such obstacles, I give (among others) memory, history or geometry, which are swamps of generalization from which one might pull out parodies of ideas (which are ghosts) but never an idea in itself. To achieve this clarity is, inevitably, to be understood."

— Mark Rothko, The Tiger's Eye, 1, no. 9 (October 1949), p. 114

Whether Holly's concept "the day that I die" is a mere parody of an idea or "an idea in itself," the reader may judge.  The reader may also judge the wisdom of building a chapel to illustrate the clarity of thought processes such as Rothko's in 1949.  I personally feel that someone who can call geometry a "swamp" may not be the best guide to religious meditation.

For another view, see this essay by Erik Anderson Reece.

Saturday, October 19, 2002

Saturday October 19, 2002

Filed under: General — m759 @ 7:47 AM

Mass Confusion

From Garrison Keillor’s Writer’s Almanac:

“It’s the birthday of [novelist] John le Carré, born David John Moore Cornwell, in Poole, England (1931)…. His father was a con artist who wanted his two sons to be lawyers because he thought it would come in handy. He sent them to boarding school, where they learned to speak and act like members of the British upper-class, but when they went home they knew they might have to bail him out of jail, or spend the holidays with a bunch of crooks. He learned German and became a spy, but said he ‘never did anything to alter the world order.'”

From The New York Times of Oct. 19, 2002:

“…victims of sexually abusive priests expressed despair and outrage yesterday at the Vatican’s refusal to endorse the American bishops’ zero tolerance policy….

‘This certainly sends the whole thing into wild confusion,’ said Thomas C. Fox, publisher of The National Catholic Reporter, an independent newsweekly that helped uncover the church’s sexual abuse problem nearly two decades ago. ‘It seems we haven’t moved anywhere in finding a resolution, and that makes it terribly, terribly painful. It’s like this nightmare simply won’t end.'”

Other classic Catholic quotations…

1.  “He ain’t heavy, he’s my brother.”

2.  “What is truth?”

3.  “Writers often cry ‘Truth! Truth at all costs!’ Some are sincere. Others are hypocrites. They use the truth, distort it, exploit it, for an ulterior purpose. Let us consider the case of John Cornwell….”  — Inside the Vatican 

John Cornwell recently wrote a classic study of the Roman Catholic Church, Hitler’s Pope* (Viking Press, October 1999).

According to the Daily Catholic and to Inside the Vatican, Cornwell is the brother of of spy novelist John le Carré (born David Cornwell). An article in the Jerusalem Post, however, seems to say that the spy novelist had only one brother, whose name was in fact Tony, not John.  A Sydney Morning Herald article confirms this version of the Cornwell family history.  Finally, once one learns from the Sydney article that David Cornwell’s father’s name was Ronnie, a perfected Google search reveals a Literary Encyclopedia article that seems to demonstrate conclusively that the Roman Catholic sources cited above lied about John Cornwell’s family background.  Of course, this may be wrong… Those who wish may investigate further.

* (I personally prefer Hitler’s own remarks on the Church’s “static pole,” but tastes differ.)

Wednesday, October 16, 2002

Wednesday October 16, 2002

Filed under: General — m759 @ 4:20 AM

"History is a nightmare
from which I am trying to awake"
— James Joyce in Ulysses

"Be of good cheer, Master Ridley, and play the man, for we shall this day light such a candle in England as I trust by God's grace shall never be put out."
— Hugh Latimer, former Bishop of Worcester, to his friend Nicholas Ridley, former private chaplain to Henry VIII, on the occasion of their being burned at the stake by the Roman Catholic queen Bloody Mary Tudor on October 16, 1555

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